Subdividing Causes Strange Edges / Issues on Shape
It's not the best topology but just quick example.

First thing I've done was to delete half of the mesh and add Mirror modifier to reduce work.

Next I've created Outer Edge Loop just by extruding vertices.

In the same manner I've filled rest of the mesh with faces with some Reduction Loops, this was needed for making all of the faces quads (more on this you can find on topologyguides.com).

I haven't used any "automatic" methods, it's just extruding E and filling F with a little help from F2 add-on. It's all manual work.